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GM5-7: Construct and describe simple loci.

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Elaboration on this Achievement Objective

This means that students will draw the graph of linear and simple quadratic equations. They will also be able to identify the linear equation for the graph of a given simple loci.

parabola and straight line.

 
They will also describe the common properties of points on a circle or ellipse and recognise the circle as a special case of the ellipse.

 

 

circle. 

All points on a circle are the same distance from the centre. That distance is the radius.     

 

ellipse.     

All points on an ellipse share a common sum of distances to two foci. As the foci close the ellipse “morphs” into a circle.

 

Teaching resources for this Achievement Objective
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Conic Cuts

Level Five
Geometry and Measurement
Figure It Out activities
This is a level 5 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore the properties of conic sections

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Ruler and Compass Constructions

Level Five
Geometry and Measurement
Units of Work
In this unit we use rulers and compasses to construct perpendicular lines and to bisect angles. These constructions are used to make a variety of polygons, nets and to illustrate loci.
  • Construct perpendicular bisectors of lines.
  • Construct bisectors of angles.
  • Use these skills to construct equilateral triangles and squares with a given side length, parallel lines, parallelograms and trapeziums, and regular polygons with a small number of sides.
  • Use construction techniques300
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Sailing with Maths

Level Five
Integrated
Figure It Out activities
This is a level 5 number, measurement, and geometry activity from the Figure It Out theme series.

calculate rates of speed

convert between nautical miles and metres

use scales on maps to find distances

follow instructions of compass degrees and scale distances

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Synchronised Swim Shapes

Level Five
Geometry and Measurement
The purpose of this unit is to engage students in applying their understanding of geometric thinking to design and describe formations and the translations and/or rotations needed to create those formations. This is explored in the context of choreographing a synchronised swimming routine and...
  • Find the size of angles. 
  • Describe the features of regular polygons, including the size of their interior angles. 
  • Apply knowledge of angles, quadrilaterals, and regular polygons to problem solving contexts.
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The Running track

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in an investigation that requires them to define the dimensions of the parameters necessary to construct a described locus.